Transcript Slide 1

Aim: What is the arithmetic sequence?
Do Now: Find the first four terms in the
sequence whose nth term is 4n + 3.
HW: p.256 # 4,5,6,8,10,12,16,18,19,20
7, 11, 15, 19
4
4
Each term after the first term is
four more than the previous term
4
The sequence an = 4n + 3 is an arithmetic
sequence. An arithmetic sequence has
consecutive terms with a common difference.
In this case, the common difference is 4.
For an arithmetic sequence, the recursive
formula is: an = a1 + d(n – 1)
Where d is the common difference
For the arithmetic sequence 100, 97, 94, 91,…,
find : a) the common difference
b) the 20th term of the sequence
d=–3
a20 = a1 + d(n – 1) = 100 + -3(20 – 1)
= 100 + -3(19) = 100 – 57 = 43
The 4th term of an arithmetic sequence is 80
and the 12th term is 32.
a. What is the common difference?
b. What is the first term of the sequence?
a.
a4  a1  d (4 1)
80  a1  d (3)
48  3d  11d
a12  a1  d (12 1)
32  a1  d (11)
48  8d , d  6
b. 80 = a1 + 3(-6), 80 = a1 – 18, a1 = 98
If 4 and 28 are the 1st and 5th terms of an
arithmetic sequence, find the 2nd, 3rd and 4th
terms of the sequence.
Use the recursive formula to find d
a5  a1  d (5 1),
4d  24, d  6
28  4  d (4),
a2  10, a3  16, a4  22
The numbers 10, 16 and 22 are called
arithmetic means between 4 and 28. An
arithmetic mean is the average of the term
before it and the term after it.
Scott is saving to buy a guitar. In the first week,
he put aside $42 that he received for his
birthday, and in each of the following weeks,
he added $8 to his savings. He needs $400 for
the guitar that he wants. In which week will he
have enough money for the guitar?
Let a1 = 42 and d = 8 then an = 400
an  42  8(n 1)
400  42  8(n  1)
400  42  8n  8
8n  366, n  45.75
46th week
1. Given an arithmetic sequence 3,6,9,12,…, n = 8
a. Find the common difference
b. Write the nth term formula
c. Find the value of 8th term
d=3
an = 3 + 3(n – 1)
a8 = 24
2. Write the first six terms of the arithmetic sequence
that has 12 for the first term and 42 for the six term.
12, 18, 24, 30, 36, 42
3. Find four arithmetic means between 3 and 18
6, 9, 12, 15